A Logic of Trust and Reputation

Transcription

1 A Logic of Trust and Reputation Emiliano Lorini (joint work with A. Herzig, J. F. Hübner, L. Vercouter) IRIT-CNRS, Toulouse, France Workshop on Trust, Advice, and Reputation Toulouse, October 2009

2 Motivation: formal analysis of trust and reputation many computational models [Sabater & Sierra 02; Huynh et al. 04] quantitative no qualitative analysis few logical models mostly focused on trust in information sources [Liau 03; Jones & Firozabadi 01; Dastani et al. 04] cognitive model of trust [Castelfranchi & Falcone 98, 01] informal definitions formal definitions? relations between trust and reputation?

3 Contribution: definitions in a BDI logic [Lorini & Demolombe 2008, 2009; Lorini, Falcone, Castelfranchi 2008; Herzig, Lorini, Hübner, Vercouter 2009] top-down qualitative analysis: reduction of trust to more primitive concepts trust belief, goal, intention, action analysis in terms of logics of action and time, BDI logics two versions of trust occurrent trust vs. dispositional trust refinement of Castelfranchi & Falcone s definition from dispositional trust to reputation

4 Trust: the ingredients [Castelfranchi & Falcone] i trusts j to do α in order to achieve ϕ truster i, trustee j, action α of j, goal ϕ of i. important: trust thinking and foreseeing

5 Informal definition [Castelfranchi & Falcone] trust evaluation of the truster about certain properties of trustee (that are relevant for a goal/task ϕ) i trusts j to do α in order to achieve ϕ if and only if: 1 i has the goal ϕ; 2 i believes that 1 j is capable to do α; 2 j has the power to achieve ϕ by doing α; 3 j intends to do α. trust defined from four more primitive concepts logic of goal, ability, power and intention?

6 1 Two kinds of trust: occurrent vs. dispositional 2 Logical formalization 3 From trust to reputation 4 Conclusion

7 Two kinds of trust: occurrent vs. dispositional

8 Occurrent trust vs. dispositional trust two perspectives on trustee s action α: truster believes trustee is going to do α here and now occurrent trust truster believes trustee is going to do α whenever some conditions are satisfied. dispositional trust (cf. occurrent belief vs. dispositional belief [Searle 92])

9 Occurrent trust i wants ϕ to be true and believes j is going to perform α here and now so that ϕ will be ensured OccTrust(i, j, α, ϕ) def = OccGoal(i, ϕ) Belief (i, OccCap(j, α) OccPower(j, α, ϕ) OccIntends(j, α)) predicates to be defined: Belief, OccGoal, OccCap, OccPower, OccIntends

10 Example 1 s occurrent trust in 2 to send a certain product in view of satisfying 1 s goal of possessing the product: 1 wants to possess the product, 1 believes that 2 is capable to send the product, 2 s act of sending the product will result in 1 possessing it, 2 has the intention to send the product.

11 Dispositional trust i expects that there will be some situations κ in which he will have the goal of achieving ϕ (potential goal), and believes that in all these situations j will ensure ϕ by doing action α DispTrust(i, j, α, ϕ, κ) def = PotGoal(i, ϕ, κ) Belief (i, Henceforth ((κ OccGoal(i, ϕ)) (OccCap(j, α) OccPower(j, α, ϕ) OccIntends(j, α))) predicates to be defined: PotGoal, Belief, Henceforth, OccGoal, OccCap, OccPower, OccIntends

12 Example 1 s dispositional trust in 2 (a mechanic) to repair his car so that the car will be in order, in the circumstances in which 1 will ask the mechanic to repair his car

13 Logical formalization

14 Occurrent trust and dispositional trust: components definiendum: belief, occurrent goal, occurrent capability, occurrent power, occurrent intention. definiens: formulas of a modal logic of time, belief, preference, and action spell out predicates Belief (i, ϕ), OccGoal(i, ϕ), PotGoal(i, ϕ, κ), OccCap(j, α), OccPower(j, α, ϕ), OccIntends(j, α) using modal operators of time, belief, preference, and action convention: Bel i, etc. = logical operators

15 Temporal operators Henceforth ϕ = ϕ henceforth holds Eventually ϕ def = Henceforth ϕ Eventually ϕ = ϕ eventually holds will be used to define OccGoal(i, ϕ), etc.

16 Belief operators Bel i ϕ = agent i believes that ϕ Poss i ϕ def = Bel i ϕ Poss i ϕ = agent i thinks that ϕ is possible epistemic and doxastic logic [Hintikka 62] express truster s beliefs about trustee s properties Belief (i, ϕ) def = Bel i ϕ

17 Goals as preferences about the future Pref i ϕ = agent i wants ϕ to be true binary preferences [Cohen & Levesque 90] positive introspection: Pref i ϕ Bel i Pref i ϕ negative introspection: Pref i ϕ Bel i Pref i ϕ realism: Bel i ϕ Pref i ϕ OccGoal(i, ϕ) def = Pref i Eventually ϕ

18 Capability in dynamic logic After i:α ϕ = ϕ will be true after every possible execution of action α by agent i propositional dynamic logic (PDL) formulas = ϕ, ψ,... = state descriptions actions = α, β,... = state transition descriptions action formula i : α = action α with author i After i:α = i cannot do α OccCap(j, α) def = After j:α j is capable to perform α = j can do α

19 Power in dynamic logic OccPower(j, α, ϕ) def = After j:α ϕ relates j s action α with i s goal ϕ missing: epistemic aspect of power ( knowing how to play )

20 Intention-to-do as preferred action Does i:α ϕ = agent i is going to do α and ϕ will be true afterwards Does i:α = i does α OccIntends(j, α) def = Pref j Does j:α Some axioms: Theorem 1 Does i:α ϕ After i:α ϕ ( Does i:α After i:α ) 2 (Pref i Does i:α After i:α ) Does i:α 3 Does i:α Pref i Does i:α (Pref i Does i:α After i:α ) Does i:α

21 Formal definition of occurrent trust OccTrust(i, j, α, ϕ) def = Pref i Eventually ϕ Bel i ( After j:α After j:α ϕ Pref j Does j:α )

22 Example 1 s occurrent trust in 2 to send a certain product in view of satisfying 1 s goal of possessing the product OccTrust(1, 2, sendp1, hasp1) def = Pref 1 Eventually hasp1 Bel 1 ( After 2:sendP1 After 2:sendP1 hasp1 Pref 2 Does 2:sendP1 )

23 Some properties of occurrent trust Theorem OccTrust(i, j, α, ϕ) (Pref i Eventually ϕ Bel i (Does i:α After j:α ϕ)) OccTrust(i, j, α, ϕ) Bel i OccTrust(i, j, α, ϕ) OccTrust(i, j, α, ϕ) Bel i Eventually ϕ

24 Potential goal PotGoal(i, ϕ, κ) def = Poss i Eventually (κ Pref i Eventually ϕ)

25 Formal definition of dispositional trust DispTrust(i, j, α, ϕ, κ) def = Poss i Eventually (κ Pref i Eventually ϕ) Bel i Henceforth ((κ Pref i Eventually ϕ) ( After j:α After j:α ϕ Pref j Does j:α ))

26 Example 1 s dispositional trust in 2 (a mechanic) to repair his car so that the car will be in order, in the circumstances in which 1 will ask the mechanic to repair his car DispTrust(1, 2, rep1c, OK1c, ask12) def = Poss 1 Eventually (ask12 Pref 1 Eventually OK1c) Bel 1 Henceforth ((ask12 Pref 1 Eventually OK1c) ( After 2:rep1c After 2:rep1c OK1c Pref 2 Does 2:rep1c ))

27 Some properties of dispositional trust Theorem DispTrust(i, j, α, ϕ, κ) (Poss i Eventually (κ Pref i Eventually ϕ) Bel i Henceforth ((κ Pref i Eventually ϕ) (Does i:α After j:α ϕ))) DispTrust(i, j, α, ϕ, κ) Bel i DispTrust(i, j, α, ϕ, κ)

28 From dispositional to occurrent trust Theorem (DispTrust(i, j, α, ϕ, κ) Pref i Eventually ϕ Bel i κ) OccTrust(i, j, α, ϕ)

29 Discussion: other definition of trust Deutsch s definition (1958): trust involves risk perception (trusting is doing a real bet on the trustee) Uncertain beliefs are needed to capture it Genuine trust (Trust game, Baier 1986, Holton 1994): i s belief that j has goodwill towards him (j is willing to sacrifice his wellbeing for i) It is just a special case of our definition Jones s definition (2002): rule belief+conformity belief Trust thinking or foreseeing

30 From trust to reputation

31 Reputation: the building blocks Rep(I, j, α, ϕ, κ) = j has reputation in group I to ensure ϕ by doing α in the circumstances κ Reputation as the collective counterpart of trust TRUST = agent i s individual evaluation (belief) about some properties of agent j that are relevant for a goal of i REPUTATION = group I s collective evaluation about some properties of agent j that are relevant for a (group) goal of I to be defined: collective evaluation, group goals

32 Public facts For every I such that I > 2, Public I ϕ = ϕ is public in the group of agents I ( ϕ is said in I ) ϕ is public in I common belief in I that ϕ ϕ is public in I does not imply every agent in I believes ϕ

33 Logic of public facts: some principles 1 (Public I ϕ Public I ϕ) 2 Public I ϕ Public J Public I ϕ if J I 3 Public I ϕ Public J Public I ϕ if J I 4 Public I ϕ Bel i Public I ϕ if i I 5 Public I ϕ Bel i Public I ϕ if i I 6 Public I ( i I Bel i ϕ ϕ)

34 Group goals GroupPref I ϕ = the agents in I want that ϕ group goals: broad sense (individual preference aggregation) weaker than joint goals and joint intentions [Grosz & Kraus 96] Some examples of GroupPref I ϕ definition: -group goal: i I Pref i ϕ -group goal: i I Pref i ϕ Group goal based on majority: J I, J > I\J i J Pref i ϕ

35 Formal definition of reputation Rep(I, j, α, ϕ, κ) def = PotGoal(I, ϕ) Poss I Henceforth ((κ GroupPref I Eventually ϕ) ( After j:α After j:α ϕ Pref j Does j:α )) Poss I ϕ def = Public I ϕ Poss I ϕ = according to the group I, ϕ is possible PotGoal(I, ϕ) def = Poss I Eventually (κ GroupPref I Eventually ϕ)

36 Conclusion

37 Conclusion Contribution. formal definitions of occurrent trust and dispositional trust formal definition of reputation and its relation with trust Our related works semantics for the different modalities mathematical properties of the logic of belief, preference, action and time (soundness, completeness) trust in information sources and in communication systems from binary trust to graded trust trust in agents vs. trust in roles Implementation of a BDI agent reasoning about trust (see Vercouter s presentation)

38 THANK YOU!